A336918 - OEIS

%I #11 Aug 17 2020 20:52:08

%S 1,2,3,5,6,7,8,10,11,12,13,14,15,17,19,21,22,23,24,25,26,27,28,29,30,

%T 31,33,34,35,37,38,39,40,41,42,43,46,47,50,51,52,53,54,55,56,57,58,59,

%U 60,61,62,63,65,66,67,69,70,71,73,74,75,76,77,78,79,82,83,84,85,86,87,88,89,91,92,93,94,95,96,97,101

%N Numbers k such that A000005(k) divides A003973(k); numbers k for which A336839(k) = 1.

%C Numbers k such that A003961(k) is in A003601. Numbers which become (or stay as) arithmetic numbers when all primes in their prime factorization are replaced by the next larger primes.

%C Numbers k for which A003973(k) is equal to A000005(k)*A336838(k).

%H Antti Karttunen, <a href="/A336918/b336918.txt">Table of n, a(n) for n = 1..10000</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Arithmetic_number">Arithmetic number</a>

%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

%o (PARI)

%o A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };

%o isA336918(n) = !(sigma(A003961(n))%numdiv(n));

%Y Cf. A000005, A003601, A003961, A003973, A336838, A336930.

%Y Positions of ones in A336839.

%Y Cf. A336919 (complement).

%K nonn

%O 1,2

%A _Antti Karttunen_, Aug 12 2020